Mathematical Modelling and Methods for Load Balancing and Coordination of Multi-Robot Stations
Doctoral thesis, 2022
The automotive industry is moving from mass production towards an individualized production, individualizing parts aims to improve product quality and to reduce costs and material waste. This thesis concerns aspects of load balancing and coordination of multi-robot stations in the automotive manufacturing industry, considering efficient algorithms required by an individualized production. The goal of the load balancing problem is to improve the equipment utilization. Several approaches for solving the load balancing problem are suggested along with details on mathematical tools and subroutines employed.
Our contributions to the solution of the load balancing problem are fourfold. First, to circumvent robot coordination we construct disjoint robot programs, which require no coordination schemes, are flexible, admit competitive cycle times for several industrial instances, and may be preferred in an individualized production. Second, since solving the task assignment problem for generating the disjoint robot programs was found to be unreasonably time-consuming, we model it as a generalized unrelated parallel machine problem with set packing constraints and suggest a tailored Lagrangian-based branch-and-bound algorithm. Third, a continuous collision detection method needs to determine whether the sweeps of multiple moving robots are disjoint. We suggest using the maximum velocity of each robot along with distance computations at certain robot configurations to derive a function that provides lower bounds on the minimum distance between the sweeps. The lower bounding function is iteratively minimized and updated with new distance information; our method is substantially faster than previously developed methods. Fourth, to allow for load balancing of complex multi-robot stations we generalize the disjoint robot programs into sequences of such; for some instances this procedure provides a significant equipment utilization improvement in comparison with previous automated methods.
Our contributions to the solution of the load balancing problem are fourfold. First, to circumvent robot coordination we construct disjoint robot programs, which require no coordination schemes, are flexible, admit competitive cycle times for several industrial instances, and may be preferred in an individualized production. Second, since solving the task assignment problem for generating the disjoint robot programs was found to be unreasonably time-consuming, we model it as a generalized unrelated parallel machine problem with set packing constraints and suggest a tailored Lagrangian-based branch-and-bound algorithm. Third, a continuous collision detection method needs to determine whether the sweeps of multiple moving robots are disjoint. We suggest using the maximum velocity of each robot along with distance computations at certain robot configurations to derive a function that provides lower bounds on the minimum distance between the sweeps. The lower bounding function is iteratively minimized and updated with new distance information; our method is substantially faster than previously developed methods. Fourth, to allow for load balancing of complex multi-robot stations we generalize the disjoint robot programs into sequences of such; for some instances this procedure provides a significant equipment utilization improvement in comparison with previous automated methods.
makespan minimization
Smart Assembly 4.0
Voronoi diagram
decomposition
automotive manufacturing
mathematical modelling
vehicle routing
motion planning
set packing
continuous collision detection
Pascal,Chalmers campus Johanneberg, Chalmers tvärgata 3
Opponent: Professor Martin Skutella, Institute of Mathematics, TU Berlin, Germany
Author
Edvin Åblad
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Fraunhofer-Chalmers Centre
Intersection-Free Geometrical Partitioning of Multirobot Stations for Cycle Time Optimization
IEEE Transactions on Automation Science and Engineering,;(2018)
Journal article
Exact makespan minimization of unrelated parallel machines
Open Journal of Mathematical Optimization,;Vol. 2(2021)
Journal article
Continuous collision detection of pairs of robot motions under velocity uncertainty
IEEE Transactions on Robotics,;Vol. 37(2021)p. 1780-1791
Journal article
Spatial–temporal load balancing and coordination of multi-robot stations
IEEE Transactions on Automation Science and Engineering,;Vol. 20(2023)p. 2203-2214
Journal article
E. Åblad, A.-B. Strömberg, D. Spensieri A Lagrangian-based method for makespan minimization of parallel machines with set packing constraints
Preventing collisions in multi-robot stations
In the automotive industry, it is desired to decrease the time from initial concept to final product. Moreover, the parts of a product have small deviations, hence tailoring each individual product, e.g., its welding program, can improve both quality and cost. To meet such demands with a high throughput, the decision process needs to be fully automated.
In multi-robot stations of manufacturing lines, robotics arms are positioned around the workpiece on which they carry out a set of (weld) tasks.
To maximize the throughput: the tasks are assigned to the robots, the order of the tasks is specified, and collision-free motions of the robots are computed. The robots may not collide with each other, hence the motion (and its duration) of a robot depend on the motions of the other robots, making the problem hard to solve optimally.
A common approach to solve the problem is to initially assume that the robots will not collide, and then let the robots wait on another to prevent collisions. This approach is computationally efficient since the robots’ motions can be computed independently, but it can lead to poor solutions.
In this thesis, the robots are instead constrained to work in separate volumes, thus preventing any robot-robot collisions. These volumes may change over time. This new approach allows for finding good solutions to some challenging scenarios, and thus, allowing for a higher degree of automation.
In the automotive industry, it is desired to decrease the time from initial concept to final product. Moreover, the parts of a product have small deviations, hence tailoring each individual product, e.g., its welding program, can improve both quality and cost. To meet such demands with a high throughput, the decision process needs to be fully automated.
In multi-robot stations of manufacturing lines, robotics arms are positioned around the workpiece on which they carry out a set of (weld) tasks.
To maximize the throughput: the tasks are assigned to the robots, the order of the tasks is specified, and collision-free motions of the robots are computed. The robots may not collide with each other, hence the motion (and its duration) of a robot depend on the motions of the other robots, making the problem hard to solve optimally.
A common approach to solve the problem is to initially assume that the robots will not collide, and then let the robots wait on another to prevent collisions. This approach is computationally efficient since the robots’ motions can be computed independently, but it can lead to poor solutions.
In this thesis, the robots are instead constrained to work in separate volumes, thus preventing any robot-robot collisions. These volumes may change over time. This new approach allows for finding good solutions to some challenging scenarios, and thus, allowing for a higher degree of automation.
Interlinked combinatorial and geometrical optimization problems in an autonomous automotive manufacturing industry
Swedish Foundation for Strategic Research (SSF) (RIT15-0025), 2017-08-15 -- 2022-09-05.
Fraunhofer-Chalmers Centre, 2017-08-15 -- 2022-09-05.
Smart Assembly 4.0
Swedish Foundation for Strategic Research (SSF) (RIT15-0025), 2016-05-01 -- 2021-06-30.
Driving Forces
Sustainable development
Areas of Advance
Production
Subject Categories
Computational Mathematics
Robotics
ISBN
978-91-7905-661-2
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5127
Publisher
Chalmers
Pascal,Chalmers campus Johanneberg, Chalmers tvärgata 3
Opponent: Professor Martin Skutella, Institute of Mathematics, TU Berlin, Germany